APOD: Atoms for Peace Galaxy Collision (2010 Nov 16)

[Chris Peterson]

OK, makes sense, but in my naive thinking, I would think the small scale of our slice of the pie, would make the measurements impossible with our current technology. *I don't know... just thinking out loud, so to speak.*

Well, if the size of our scale was changing, and we needed to rely on something like redshift, you're probably correct. But as Neufer calculated, the sort of growth rate we'd expect within this part of the Solar System is measured in millimeters, which is well within our ability to measure, assuming that our reference isn't changing along with everything else.

One more question, regarding time/space and expansion. What are the popular beliefs about this? Is it believed that time/space expand, and if so, at what speed, relative to the matter of the universe.

Space-time is the fabric of the Universe, and as it expands it carries matter along with it. So neither is moving with respect to the other. We measure expansion by looking at recession velocity versus distance, relative to us. The rate is given by Hubble's law, and is not in units of velocity, but of velocity divided by distance.

I'd think if they were expanding at the same speed, there would be no observable red shift.

Keep in mind that redshift is not caused by the Doppler effect. It occurs because the space through which the light is traveling has expanded between the time the photon was emitted, and the time it is observed. That stretching of space increases the wavelength of the light.

[ZenGrouch]

Keep in mind that redshift is not caused by the Doppler effect. It occurs because the space through which the light is traveling has expanded between the time the photon was emitted, and the time it is observed. That stretching of space increases the wavelength of the light.

Looks like I've learned a biggie today... I'd always worked under the assumption that the red shift was caused by the Doppler effect.

Time to hit the library.

Thanks for your help!

[neufer]

Laser reflectors on the moon indicate that the Moon is spiraling away from Earth at a rate of 38 mm per year.
Perhaps 28 mm per year is due to Hubble expansion and only 10 mm per year is due to tidal forcing.

I believe that the measured 38mm per year is very consistent with our understanding of momentum transfer and does not require any assumption about the expansion of space. I also believe that assuming the expansion of space to be happening between the Earth and Moon breaks GR, which seems to me a very unlikely thing.

You had previously agreed that the expansion of space takes place at all dimensions
and is thereby responsible for Hubble redshift (wavelength increase) itself.

The Hubble constant of 10.8 (m/yr)/AU = 10.8 (m/yr)/[149,600,000,000 m]
~ 1 part in 13.8 billion per year (consistent with the age of the universe).

Assuming the earth itself expands at 1 part in 13.8 billion per year
then the earth's moment of inertia increases at 1 part in 6.9 billion per year;
hence, the earth's rotation period increases at 1 part in 6.9 billion per year.

The measured length of a day is increasing by
0.0017 seconds per century which is about 1 part in 5 billion per year.

So the measured increase in the length of a day (by 1 part in 5 billion per year)
is also primary due to Hubble expansion rather than tidal forces

[Chris Peterson]

You had previously agreed that the expansion of space takes place at all dimensions
and is thereby responsible for Hubble redshift (wavelength increase) itself.

I don't recall making any such statement. What I said was that local gravity fields limit the expansion of space-time. That has an insignificant impact on cosmological redshift.

I do not believe that the expansion of space is the same everywhere.

[neufer]

You had previously agreed that the expansion of space takes place at all dimensions
and is thereby responsible for Hubble redshift (wavelength increase) itself.

I don't recall making any such statement.
What I said was that local gravity fields limit the expansion of space-time.
That has an insignificant impact on cosmological redshift.

I do not believe that the expansion of space is the same everywhere.

Then, pray tell, what causes Hubble redshift
if it is not the fundamental increase of the photon's wavelength?

And why is my calculation of the Hubble relative effect on the observed increase in the moon's orbit [2.8/3.8 ~ 73%]
so close to my calculation of the Hubble relative effect on the observed increase in the earth's day [5/6.9 ~ 73%]
[Hence, only about 27% is due to tidal coupling.]

I.e., where am I going wrong?

[Chris Peterson]

Then, pray tell, what causes Hubble redshift
if it is not the fundamental increase of the photon's wavelength?

Yes. What does that have to do with the fact that gravity overcomes cosmological expansion on a local scale?

And why is my calculation of the Hubble relative effect on the observed increase in the moon's orbit [2.8/3.8 ~ 73%]
so close to my calculation of the Hubble relative effect on the observed increase in the earth's day [5/6.9 ~ 73%] :?:
[Hence, only about 27% is due to tidal coupling.]

I.e., where am I going wrong?

I'd say you're going wrong by making the assumption that any of the separation is related to cosmological expansion. The guys who play with the dimensions of the Pyramids can provide all sorts of amazing correlations, too! And why do you assume a linear relationship between the Moon's orbital radius and the length of the Earth's day?

[neufer]

Then, pray tell, what causes Hubble redshift
if it is not the fundamental increase of the photon's wavelength?

Yes. What does that have to do with the fact that gravity overcomes cosmological expansion on a local scale?

Hubble expansion is generally insignificant over distances & times
that are small compared with the size & age of the universe.

But that does not mean that Hubble expansion doesn't exist on the scale
of even photons (as it must to explain the non-Doppler Hubble redshift).

Hubble expansion on the scale of the Earth Moon dynamic system (over decades) seems to be just measurable.

And why is my calculation of the Hubble relative effect on the observed increase in the moon's orbit [2.8/3.8 ~ 73%]
so close to my calculation of the Hubble relative effect on the observed increase in the earth's day [5/6.9 ~ 73%]
[Hence, only about 27% is due to tidal coupling.]

I.e., where am I going wrong?

I'd say you're going wrong by making the assumption that any of the separation is related to cosmological expansion. The guys who play with the dimensions of the Pyramids can provide all sorts of amazing correlations, too! And why do you assume a linear relationship between the Moon's orbital radius and the length of the Earth's day?

The generally held assumption is that tidal effects are totally responsible for
the increase in both the Moon's orbital radius & the length of the Earth's day.

But Hubble expansion should also affect both the Moon's orbital radius & the length of the Earth's day.

My back of the envelope calculations seem to indicate that Hubble expansion dominates both
while being qualitatively indistinguishable from tidal effects (over decadal time periods).
......................................................................................................
Note that the increased tidal effects of the past would have placed
the moon very close to the Earth just two billion years ago.

The fact that current tidal force amounts to only 10 mm/yr expansion rather than 38 mm/yr expansion
would help explain why the moon was not so uncomfortably close to the Earth just two billion years ago.

[Chris Peterson]

But that does not mean that Hubble expansion doesn't exist on the scale
of even photons (as it must to explain the non-Doppler Hubble redshift).

The issue isn't whether time-space expands on very small scales. It certainly does. The issue is whether it expands in regions with strong gravitational fields, and my understanding is that it does not. Galaxies in clusters are not receding from each other. Planets around stars aren't getting larger orbits.

The generally held assumption is that tidal effects are totally responsible for
the increase in both the Moon's orbital radius & the length of the Earth's day.

But Hubble expansion should also affect both the Moon's orbital radius & the length of the Earth's day.

The generally held assumption about tidal effects is held because the calculation of the effect is consistent with the observed magnitude. The fact that the calculation for increasing separation from Hubble's law is similar to the observed value does not convince me that there is any cosmological expansion between the Earth and Moon. Have you applied this method to the other planets of the Solar System? Are they receding from the Sun by the expected amounts? Uranus should be receding at 324 m/y, which sounds like a lot, a detectable amount. That's a couple of AU per billion years- something I haven't seen accounted for in Solar System evolution models.

[neufer]

But that does not mean that Hubble expansion doesn't exist on the scale
of even photons (as it must to explain the non-Doppler Hubble redshift).

The issue isn't whether time-space expands on very small scales. It certainly does. The issue is whether it expands in regions with strong gravitational fields, and my understanding is that it does not. Galaxies in clusters are not receding from each other. Planets around stars aren't getting larger orbits.

The Andromeda Galaxy is receding from us by 55 km/sec thanks to Hubble expansion.

But the relative (random?) velocity of the Andromeda Galaxy is hundreds of kilometers per second
such that the 55 km/sec Hubble expansion is obscured...BUT IT STILL EXISTS NONETHELESS

Just because Hubble expansion gets lost in the noise of overall general dynamics
inside of 1 Mpc does not imply that it is being canceled out somehow.

Likewise, planets around stars are getting larger orbits by 10.8 (m/yr)/AU
and planetary sidereal periods are getting longer by 1 part in 9.2 billion (i.e., 0.07 mas per orbit²).
...but it is very difficult to measure such things (even for the earth).

The generally held assumption is that tidal effects are totally responsible for
the increase in both the Moon's orbital radius & the length of the Earth's day.

But Hubble expansion should also affect both the Moon's orbital radius & the length of the Earth's day.

The generally held assumption about tidal effects is held because the calculation of the effect is consistent with the observed magnitude.

To what accuracy? A factor of two? Can you site a reference?

The fact that the calculation for increasing separation from Hubble's law is similar to the observed value does not convince me that there is any cosmological expansion between the Earth and Moon. Have you applied this method to the other planets of the Solar System? Are they receding from the Sun by the expected amounts? Uranus should be receding at 324 m/y, which sounds like a lot, a detectable amount. That's a couple of AU per billion years- something I haven't seen accounted for in Solar System evolution models.

Uranus in opposition is receding from the earth at 197 m/y, which may sounds like a lot but...
none of the gas giants have any hard surface off of which to bounce radar waves.

(A multi-year stationary transponder on the surface of Mars would certainly be a help.)

[Chris Peterson]

The Andromeda Galaxy is receding from us by 55 km/sec thanks to Hubble expansion...

Sorry, I don't buy any of it. If the Earth were expanding at the rate predicted by Hubble's law, it would be readily detectable by laboratory interferometry. The amount would be well inside the sensitivity of LIGO, but I've never seen that LIGO has plans to make this measurement, nor is correction for cosmological expansion listed in the (long!) list of factors that LIGO has to compensate for. This is also true for LISA, the proposed space-based gravity wave detector.

Everything I know about GR makes me believe that gravitational fields overcome cosmological expansion, and that space-time itself is expanding at less than the Hubble rate where gravitational fields are strong. I might be completely wrong about that, but I haven't seen anything to convince me otherwise, yet.

[neufer]

The Andromeda Galaxy is receding from us by 55 km/sec thanks to Hubble expansion...

Sorry, I don't buy any of it.

Don't be sorry. This is what makes science interesting. (And it helps me to learn the fastest.)

If the Earth were expanding at the rate predicted by Hubble's law, it would be readily detectable by laboratory interferometry. The amount would be well inside the sensitivity of LIGO, but I've never seen that LIGO has plans to make this measurement, nor is correction for cosmological expansion listed in the (long!) list of factors that LIGO has to compensate for. This is also true for LISA, the proposed space-based gravity wave detector.

LIGO isn't sensitive to low frequencies.
In any event, the expansion of the Earth is the part that I am least confident about.

I would bet the farm, however, on the Moon receding due to Hubble expansion.

Assuming that a R^-6 quadrupole-quadrupole interaction for the
feedback tidal force the moon's distance would be tidally growing as R ~ t^1/7.

This motion would be catastrophic for the Moon about 2 billion years ago
if the current tidal expansion rate was the full 38 mm/yr.

Having the current tidal expansion rate at just 10 mm/yr
makes for a much more contented lunar past.

Everything I know about GR makes me believe that gravitational fields overcome cosmological expansion, and that space-time itself is expanding at less than the Hubble rate where gravitational fields are strong. I might be completely wrong about that, but I haven't seen anything to convince me otherwise, yet.

What mechanism would cause local gravitational fields to cancel the Hubble rate?

Why would such a purported mechanism have no effect on the wavelength of photons.

[Chris Peterson]

What mechanism would cause local gravitational fields to cancel the Hubble rate?

My understanding is that this is intrinsic to the equations of GR. And while I think I have a better than average understanding of GR, I certainly don't have the mathematical skills to do the actual tensor calculus, or even to fully grok the equations at that level. So I'm left with my basic, far from comprehensive understanding of this from more general reading.

Why would such a purported mechanism have no effect on the wavelength of photons.

I can't think of a case where photons arriving from cosmological distances would have any significant percentage of their path passing through strong gravitational fields. "Strong", as I understand it in this case, is the sort of fields encountered in galaxy clusters.

From a purely observational standpoint, I think that if planetary orbits in the Solar System were actually increasing by tens or hundreds of meters per year as you suggest, this would show up in patterns of meteorite impacts as well as various long term models, as the positions of resonance radii in the asteroid belt shifted. These expansion rates translate to AUs per billion years.

[neufer]

What mechanism would cause local gravitational fields to cancel the Hubble rate?

My understanding is that this is intrinsic to the equations of GR. And while I think I have a better than average understanding of GR, I certainly don't have the mathematical skills to do the actual tensor calculus, or even to fully grok the equations at that level. So I'm left with my basic, far from comprehensive understanding of this from more general reading.

Like my confusion about galaxies & planets appearing brighter in large telescopes just because it seems logical and unresolved stars themselves must appear brighter, I think that in this case you have taken the correct knowledge that Hubble expansion is by and large negligible for dynamics on the scale of local clusters and smaller to mean that there is actually NO Hubble expansion at such a scale (when this cannot be so). Just because there is a scale for insects below which surface tension dominate gravitation does not mean that the gravitational force actually somehow disappears at such small scales; it just ceases to be very important.

Why would such a purported mechanism have no effect on the wavelength of photons.

I can't think of a case where photons arriving from cosmological distances would have any significant percentage of their path passing through strong gravitational fields. "Strong", as I understand it in this case, is the sort of fields encountered in galaxy clusters.

Everywhere one looks there are galaxy clusters. Do you think that they correct the z factor of distant galaxies that are gravitationally lensed to take into account the (different) low Hubble expansion rate they must have experienced? How would the recognize the different images of the same galaxy unless they had exactly the same z regardless of which path was taken?

From a purely observational standpoint, I think that if planetary orbits in the Solar System were actually increasing by tens or hundreds of meters per year as you suggest, this would show up in patterns of meteorite impacts as well as various long term models, as the positions of resonance radii in the asteroid belt shifted. These expansion rates translate to AUs per billion years.

Only for the gas giants which have had all sorts of such movements over their lifetime.

<<The Big Rip is a cosmological hypothesis about the ultimate fate of the universe in which the matter of the universe, from stars and galaxies to atoms and subatomic particles, are progressively torn apart by the expansion of the universe at a certain time in the future. Theoretically, the scale factor of the universe becomes infinite at a finite time in the future. The hypothesis relies crucially on the type of dark energy in the universe. The key value is the equation of state parameter w, the ratio between the dark energy pressure and its energy density. At w < −1, the universe will eventually be pulled apart. Such energy is called phantom energy, an extreme form of quintessence.

In a phantom-energy dominated universe, the universe expands at an ever-increasing rate. However, this implies that the size of the observable universe is continually shrinking; the distance to the edge of the observable universe which is moving away at the speed of light from any point gets ever closer. When the size of the observable universe is smaller than any particular structure, then no interaction between the farthest parts of the structure can occur, neither gravitational nor electromagnetic (nor weak or strong), and when they can no longer interact with each other in any way they will be "ripped apart". The model implies that after a finite time there will be a final singularity, called the "Big Rip", in which all distances diverge to infinite values.>>

[Chris Peterson]

Like my confusion about galaxies & planets appearing brighter in large telescopes just because it seems logical and unresolved stars themselves must appear brighter, I think that in this case you have taken the correct knowledge that Hubble expansion is by and large negligible for dynamics on the scale of local clusters and smaller to mean that there is actually NO Hubble expansion at such a scale (when this cannot be so).

I may be misunderstanding this, but if so, that isn't the basis of my misunderstanding. As I learned this, the distorted space-time is not showing the same expansion that flat space-time shows. Gravity is very literally holding space-time together. I might be wrong, but it's not confusion over the scale of expansion.

Everywhere one looks there are galaxy clusters. Do you think that they correct the z factor of distant galaxies that are gravitationally lensed to take into account the (different) low Hubble expansion rate they must have experienced? How would the recognize the different images of the same galaxy unless they had exactly the same z regardless of which path was taken?

They wouldn't need to, because the only photons that would be affected at all are those which actually pass through clusters, and that part of their passage would only represent a fraction of a percent of the total path. The effect of undergoing less wavelength stretching over such a short distance would be insignificant. There really aren't galaxy clusters everywhere. Take any linear path through the Universe for a cosmological distance, and odds are it won't pass through any cluster. For all practical purposes, the entire path will lie in very, very flat space.

Only for the gas giants which have had all sorts of such movements over their lifetime.

These kinds of motion for Jupiter, or for asteroid belt objects, should have changed important resonances within the asteroid belt. But there's no evidence that they have changed over a few billion years. Granted, the evidence would be subtle, but not invisible, and is something that we might reasonably have seen in Earth's geologic record.

[neufer]

OK, I got the official answer from an old Univ. of Maryland classmate
Prof. Eric Adelberger <eric@npl.washington.edu> who wrote:

• • Dear Art,
  thanks for your question. You are correct that the expected (and observed) tidal friction effect increases the scale of the moon's orbit at a rate that is surprisingly close to the Hubble rate. However, it has nothing to do with the Hubble expansion which does not produce a first-order effect on bound systems (the size of atoms or solar systems is not growing at the Hubble rate). It is an amusing coincidence that the two rates are very similar today-however, the rate at which the lunar orbit expands is not constant over astronomical times as the tidal effects fall off at least as fast as 1/r^3.

So Chris wins again.

Well, I have other ways of dealing with Chris